What is the thinking behind the Recent Tags cloud feature on the home page? I can't see what value it adds.
I expect it's similar to the 'recent badges awarded' section; it gives a sense that 'things are happening on this website'. So in that sense it's a user interface thing, making the website feel more dynamic and exciting. And as Kev says, you might as well do something with that big blank area.
If you're not one of those people who appreciates this sense of busy-bee activity (I'm not either), then both are pointless from a functional perspective.
Before we had moderation tools, it was one way to keep an eye on tags that were being created inappropriately. For example, hyphen vs. no hyphen, abbreviations versus full spelling, or misspellings. Of course this backfired as well, when we had our share of trolls putting blatantly offensive tags into the system, and they couldn't be easily cleaned from the front page.
Now that we have moderation tools to show us newly created tags only, it's little more than a "Hey look at what we're discussing on this cool site!" bit of marketing, for people browsing to the site for the first time.
I'm guessing it's a way to see what tags are hot/most active at a point in time. Can't say I'm a huge fan of tag/category clouds myself, they just seem like a bit of flare to fill up white space. Your mileage may vary of course with regard to them.